A Neumann-Dirichlet Preconditioner for a FETI-DP Formulation of the Two-Dimensional Stokes Problem with Mortar Methods

A FETI-DP (dual-primal finite element tearing and interconnecting) formulation for the two-dimensional Stokes problem with mortar methods is considered. Separate sets of unknowns are used for velocity on interfaces, and the mortar constraints are enforced on the velocity unknowns by Lagrange multipliers. Average constraints on edges are further introduced as primal constraints to solve the Stokes problem correctly and to obtain a scalable FETI-DP algorithm. A Neumann– Dirichlet preconditioner is shown to give a condition number bound, Cmaxi=1,...,N{(1 + log (Hi/hi))}, where Hi and hi are the subdomain size and the mesh size, respectively, and the constant C is independent of the mesh parameters Hi and hi.